Population inversion two-level system I was studying the classic two-level system where population inversion can be realized through a $\pi$-pulse or Rapid Adiabatic Passage, like the landau-zener case. The professor said that such an Hamiltonian can be exactly realized experimentally. Then, I also know that, for realizing a laser, we need three levels in order to perform a population inversion, and cannot be done with only two levels. So my question is: if we can realize the population inversion in a two-level system with a simple $\pi$-pulse, why we need three levels for the laser? Maybe the word "population" has a different meaning in the two cases?
I know that with two levels we cannot realize a laser because we reach the limit when the stimulated emission is equally likely with the absorption, but then why the theory says we can do population inversion?
Sorry, I am little bit confused about that.
 A: Population inversion alone is not the sole requirement for a laser. The reason why we need at least a three-level system is because this inversion needs to provide net gain.
In a two-level system, absorption and emission have the same cross-section, which means that in the general case you maximize your population at 50%. However you talk about a specific special case where an inversion is possible (and that is true). But lets assume that you do use such a process to achieve inversion and that a laser is possible, then you start the laser action and after depletion of that inversion (which can happen really fast), you have a highly absorbing material. You were able to amplify a small signal only up to the point where the inversion was 50%, after that, your medium was solely absorbing. I am not saying it is impossible, but to achieve inversion of enough ions in an adiabatic process to then be able to drive laser action up to the 50% point is too cumbersome, inefficient and does not bring anything good to the table...and maybe to even achieve enough small signal gain with such a system, perhaps the pump would require to be so intense that it would be above the damage threshold of the medium.
The problem is that you need to keep a constant net gain level on the system to make a laser, and the reason why we need at least a three-level system, so that we can keep the medium inverted virtually the whole time. Even in q-switched lasers, as the ground state is cleared quite fast, inversion is easily had throughout the de-excitation and light amplification process (instead of capping at a 50% point).
Hope this helps.
